I'll write to the OP too, to let him know about this meta thread and its progress.

Regarding the possibility that somebody else steals Q's thesis problem, Ravi made a very nice point when we were chatting earlier: there's a definite social cost in the mathematical community to stealing a student's thesis problem. One could argue that having a public record does as much to help Q in his claim to the problems as it does to harm him by making the problems more public. That might be overstating the case a bit, but the point is that in the presence of substantive answers, I don't see a good argument in favor of leaving the questions deleted.

My vote is no. The commenter should be able to re-post whatever he wrote as a new answer. (Possibly with the help from one of the Mods to copy over his comment text so he doesn't have to re-type all of it.) So the wrong answer can stay safely deleted with no loss of information. But this is something that potentially need discussing if we decide that a deleted question can be un-deleted if someone else finds it useful.

Small side-question: when does the OP lose the ability to delete the thread? I thought if there was one answer, the thread was undeleteable. But it appears it's more complicated than that.

The OP loses the ability to delete when there is an answer with at least two upvotes.

@Anton: for frequent viewers of MO and Meta (like yours truly), your anonymising efforts are, well, somewhat pathetic. :)

Are they more pathetic than I meant for them to be? I think the details are often important, so I want them to be accessible with a small amount of effort, but I want to erect enough of an energy barrier that the conversation doesn't stray into rubbernecking at some guy who made a mistake.

Also, may I propose that said policy not extend to deleted answers?

It's hard for me to imagine an answer where the same sorts of concerns apply.

If an answer has multiple contributors, I think any one of them should have the power to undelete it. I certainly agree that there's no sense in undeleting confusing or just flat wrong answers that the owner deleted, but the hypothetical situation is that somebody honestly feels that there is some value in the deleted post and has gone out of their way to say so.

Anyway, I am in favour of your point of view. While I sympathize with Q, he or she should learn a lesson from this: that if something should be kept private, putting it on the internet is a horribly bad idea.

Also, may I propose that said policy not extend to deleted answers?

Recently a user (who I'll call Q) posted a handful of questions. The questions got pretty substantive answers, but the answers got no more than 1 upvote, probably because the questions were somewhat technical, so Q was able to delete the questions. One of the users (who I'll call A) who answered one of the questions emailed a moderator to find out what happened to his nice answer, the moderator emailed Q saying that A would like the question and answer undeleted, and Q emailed back saying effectively, "Please don't undelete that. It's a problem I'm working on with my advisor and I'm not supposed to discuss it in public."

In the spirit of open decision-making, I'm brining the issue to meta. If you're a 10k+ rep user, you can have a look at the questions and answers here, here, and here. If you're not a 10k+ rep user, you can email moderators@mathoverflow.net and one of us will direct you to some copies of the questions I've posted elsewhere.

My opinions

I'd like to undelete the questions and answers since it seems dishonest and unfair to the answerers to leave them deleted. More generally, I'm for the policy that a thread can be undeleted at the request of anybody who contributed, or anybody at all. To me, this is a natural extension of not allowing people to delete questions with substantive answers and of allowing 10k+ rep users to vote to undelete. I'd even be in favor of regularly scraping the database for deleted questions with substantive-looking answers to make sure this sort of abuse doesn't go unnoticed.